Curriculum Standards

1.1.1: knows, explains, and uses equivalent representations for rational numbers and simple algebraic expressions including integers, fractions, decimals, percents, and ratios; rational number bases with integer exponents; rational numbers written in scientific notation with integer exponents; time; and money.

Dividing Exponential Expressions

Dividing Mixed Numbers

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Estimating Sums and Differences

Exponents and Power Rules

Improper Fractions and Mixed Numbers

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Multiplying Exponential Expressions

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

Rational Numbers, Opposites, and Absolute Values

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Unit Conversions

Unit Conversions 2 - Scientific Notation and Significant Digits

1.1.2: compares and orders rational numbers, the irrational number pi, and algebraic expressions, e.g., Which expression is greater -3n or 3n? It depends on the value of n. If n is positive, 3n is greater. If n is negative, -3n is greater. If n is zero, they are equal.

Comparing and Ordering Decimals

Integers, Opposites, and Absolute Values

Rational Numbers, Opposites, and Absolute Values

1.1.3: explains the relative magnitude between rational numbers, the irrational number pi, and algebraic expressions.

Comparing and Ordering Decimals

Integers, Opposites, and Absolute Values

Rational Numbers, Opposites, and Absolute Values

1.1.4: recognizes and describes irrational numbers, e.g., sqare root of 2 is a non-repeating, non-terminating decimal; or pi is a non-terminating decimal.

1.1.5: knows and explains what happens to the product or quotient when:

1.1.5.a: a positive number is multiplied or divided by a rational number greater than zero and less than one, e.g., if 24 is divided by 1/3, will the answer be larger than 24 or smaller than 24? Explain.

Adding and Subtracting Integers

Dividing Fractions

Dividing Mixed Numbers

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying with Decimals

1.1.5.b: a positive number is multiplied or divided by a rational number greater than one,

Adding and Subtracting Integers

Dividing Fractions

Dividing Mixed Numbers

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying with Decimals

1.2.3: names, uses, and describes these properties with the rational number system and demonstrates their meaning including the use of concrete objects:

1.2.3.a: commutative, associative, distributive, and substitution properties [commutative: a + b = b + a and ab = ba; associative: a + (b + c) = (a + b) + c and a(bc) = (ab)c; distributive: a(b + c) = ab + ac; substitution: if a = 2, then 3a = 3 x 2 = 6];

Adding and Subtracting Integers

Equivalent Algebraic Expressions I

1.2.3.b: identity properties for addition and multiplication and inverse properties of addition and multiplication (additive identity: a + 0 = a, multiplicative identity: a * 1 = a, additive inverse: +5 + -5 = 0, multiplicative inverse: 8 x 1/8 = 1);

Adding and Subtracting Integers

1.4.2: performs and explains these computational procedures with rational numbers:

1.4.2.a: addition, subtraction, multiplication, and division of integers;

Adding and Subtracting Integers

Adding on the Number Line

1.4.2.b: order of operations (evaluates within grouping symbols, evaluates powers to the second or third power, multiplies or divides in order from left to right, then adds or subtracts in order from left to right);

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Order of Operations

1.4.2.c: approximation of roots of numbers using calculators;

1.4.2.d: multiplication or division to find:

1.4.2.d.i: a percent of a number, e.g., What is 0.5% of 10?;

1.4.2.d.iii: percent one number is of another number, e.g., What percent of 80 is 120?;

Percents and Proportions

Percents, Fractions, and Decimals

1.4.2.d.iv: a number when a percent of the number is given, e.g., 15% of what number is 30?;

Percents and Proportions

Percents, Fractions, and Decimals

1.4.2.e: addition of polynomials, e.g., (3x – 5) + (2x + 8).

Addition and Subtraction of Functions

Addition of Polynomials

1.4.2.f: simplifies algebraic expressions in one variable by combining like terms or using the distributive property, e.g., –3(x – 4) is the same as –3x + 12.

Equivalent Algebraic Expressions II

Simplifying Algebraic Expressions II

2.1.1: identifies, states, and continues a pattern presented in various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, graph), verbal (oral description), kinesthetic (action), and written using these attributes:

2.1.1.a: counting numbers including perfect squares, cubes, and factors and multiples with positive rational numbers (number theory).

Arithmetic Sequences

Finding Patterns

Geometric Sequences

2.1.1.c: geometric figures;

Arithmetic and Geometric Sequences

Finding Patterns

2.1.1.e: things related to daily life;

Arithmetic Sequences

Arithmetic and Geometric Sequences

Finding Patterns

Geometric Sequences

2.2.2: simplifies algebraic expressions in one variable by combining like terms or using the distributive property, e.g., --3(x - 4) is the same as --3x + 12.

Addition and Subtraction of Functions

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Operations with Radical Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

2.2.3: solves:

2.2.3.a: one- and two-step linear equations in one variable with rational number coefficients and constants intuitively and/or analytically;

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Point-Slope Form of a Line

Solving Algebraic Equations II

Solving Equations by Graphing Each Side

Solving Equations on the Number Line

Solving Two-Step Equations

Standard Form of a Line

2.2.3.b: one-step linear inequalities in one variable with rational number coefficients and constants intuitively, analytically, and graphically;

Exploring Linear Inequalities in One Variable

Linear Inequalities in Two Variables

Solving Linear Inequalities in One Variable

2.2.3.c: systems of given linear equations with whole number coefficients and constants graphically.

Cat and Mouse (Modeling with Linear Systems)

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

2.3.1: recognizes and examines constant, linear, and nonlinear relationships using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or appropriate technology.

Absolute Value with Linear Functions

Arithmetic Sequences

Compound Interest

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Slope-Intercept Form of a Line

2.3.2: knows and describes the difference between constant, linear, and nonlinear relationships.

Absolute Value with Linear Functions

Linear Functions

2.3.3: explains the concepts of slope and x- and y-intercepts of a line.

Cat and Mouse (Modeling with Linear Systems)

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Slope

Slope-Intercept Form of a Line

2.3.4: recognizes and identifies the graphs of constant and linear functions.

2.3.5: identifies ordered pairs from a graph, and/or plots ordered pairs using a variety of scales for the x- and y-axis.

City Tour (Coordinates)

Points in the Coordinate Plane

Points, Lines, and Equations

Slope

2.4.1: knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include:

2.4.1.a: process models (concrete objects, pictures, diagrams, number lines, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate grids) to model computational procedures, algebraic relationships, and mathematical relationships and to solve equations

Chocomatic (Multiplication, Arrays, and Area)

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

2.4.1.b: place value models (place value mats, hundred charts, base ten blocks, or unifix cubes) to compare, order, and represent numerical quantities and to model computational procedures;

Comparing and Ordering Decimals

2.4.1.c: fraction and mixed number models (fraction strips or pattern blocks) and decimal and money models (base ten blocks or coins) to compare, order, and represent numerical quantities;

Adding Fractions (Fraction Tiles)

Comparing and Ordering Decimals

2.4.1.e: equations and inequalities to model numerical relationships;

Comparing and Ordering Decimals

Linear Functions

2.4.1.f: function tables to model numerical and algebraic relationships

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Introduction to Functions

Points, Lines, and Equations

2.4.1.g: coordinate planes to model relationships between ordered pairs and linear equations and inequalities;

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

2.4.1.h: two- and three-dimensional geometric models (geoboards, dot paper, nets, or solids) and real-world objects to model perimeter, area, volume, surface area, and properties of two-and three-dimensional figures;

Chocomatic (Multiplication, Arrays, and Area)

Perimeter and Area of Rectangles

Prisms and Cylinders

Pyramids and Cones

Pythagorean Theorem with a Geoboard

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

2.4.1.j: geometric models (spinners, targets, or number cubes), process models (coins, pictures, or diagrams), and tree diagrams to model probability;

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

2.4.1.k: frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts, tables, single and double stem-and-leaf plots, scatter plots, box-and-whisker plots, and histograms to organize and display data;

Box-and-Whisker Plots

Compound Inequalities

Correlation

Describing Data Using Statistics

Distance-Time Graphs

Histograms

Least-Squares Best Fit Lines

Prairie Ecosystem

Reaction Time 1 (Graphs and Statistics)

Solving Using Trend Lines

Stem-and-Leaf Plots

Trends in Scatter Plots

3.1.1: recognizes and compares properties of two- and three-dimensional figures using concrete objects, constructions, drawings, appropriate terminology, and appropriate technology.

Classifying Quadrilaterals

Parallelogram Conditions

Similar Figures

Special Parallelograms

3.1.2: discusses properties of triangles and quadrilaterals related to:

3.1.2.a: sum of the interior angles of any triangle is 180°;

Isosceles and Equilateral Triangles

Polygon Angle Sum

Triangle Angle Sum

3.1.2.b: sum of the interior angles of any quadrilateral is 360°;

Classifying Quadrilaterals

Parallelogram Conditions

Polygon Angle Sum

Special Parallelograms

Triangle Angle Sum

3.1.2.c: parallelograms have opposite sides that are parallel and congruent, opposite angles are congruent;

Classifying Quadrilaterals

Parallelogram Conditions

3.1.2.d: rectangles have angles of 90°, sides may or may not be equal;

Classifying Quadrilaterals

Perimeter and Area of Rectangles

Special Parallelograms

3.1.2.e: rhombi have all sides equal in length, angles may or may not be equal;

3.1.2.f: squares have angles of 90°, all sides congruent;

Classifying Quadrilaterals

Perimeter and Area of Rectangles

Special Parallelograms

3.1.2.g: trapezoids have one pair of opposite sides parallel and the other pair of opposites sides are not parallel;

3.1.2.h: kites have two distinct pairs of adjacent congruent sides.

3.1.3: recognizes and describes the rotational symmetries and line symmetries that exist in two-dimensional figures.

Holiday Snowflake Designer

Quilting Bee (Symmetry)

3.1.5: knows and describes Triangle Inequality Theorem to determine if a triangle exists.

3.1.6: uses the Pythagorean theorem to:

3.1.6.a: determine if a triangle is a right triangle,

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

3.1.7: recognizes and compares the concepts of a point, line, and plane.

Parallel, Intersecting, and Skew Lines

3.1.9: describes and explains angle relationships:

3.1.9.a: when two lines intersect including vertical and supplementary angles;

3.1.9.b: when formed by parallel lines cut by a transversal including corresponding, alternate interior, and alternate exterior angles.

3.1.10: recognizes and describes arcs and semicircles as parts of a circle and uses the standard notation for arc and circle.

Chords and Arcs

Inscribed Angles

3.2.3: converts within the customary system and within the metric system.

3.2.5: uses given measurement formulas to find:

3.2.5.a: area of parallelograms and trapezoids;

Area of Parallelograms

Area of Triangles

Perimeter and Area of Rectangles

3.2.5.b: surface area of rectangular prisms, triangular prisms, and cylinders;

Surface and Lateral Areas of Prisms and Cylinders

3.2.5.c: volume of rectangular prisms, triangular prisms, and cylinders;

Prisms and Cylinders

Pyramids and Cones

3.2.6: recognizes how ratios and proportions can be used to measure inaccessible objects, e.g., using shadows to measure the height of a flagpole.

3.3.1: identifies, describes, and performs single and multiple transformations [reflection, rotation, translation, reduction (contraction/shrinking), enlargement (magnification/growing)] on a two-dimensional figure.

Circles

Dilations

Holiday Snowflake Designer

Reflections

Rock Art (Transformations)

Rotations, Reflections, and Translations

Similar Figures

Translations

3.3.2: describes a reflection of a given two-dimensional figure that moves it from its initial placement (preimage) to its final placement (image) in the coordinate plane over the x- and y-axis.

Dilations

Rock Art (Transformations)

Rotations, Reflections, and Translations

Translations

3.3.3: draws:

3.3.3.b: a scale drawing of a two-dimensional figure;

3.3.3.c: a two-dimensional drawing of a three-dimensional figure.

Surface and Lateral Areas of Prisms and Cylinders

3.4.1: uses the coordinate plane to:

3.4.1.a: list several ordered pairs on the graph of a line and finds the slope of the line;

Cat and Mouse (Modeling with Linear Systems)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Point-Slope Form of a Line

Points, Lines, and Equations

Slope

Slope-Intercept Form of a Line

Standard Form of a Line

3.4.1.e: solve simple systems of linear equations.

Solving Linear Systems (Matrices and Special Solutions)

3.4.2: uses a given linear equation with integer coefficients and constants and an integer solution to find the ordered pairs, organizes the ordered pairs using a T-table, and plots the ordered pairs on a coordinate plane.

4.1.1: knows and explains the difference between independent and dependent events in an experiment, simulation, or situation.

Independent and Dependent Events

4.1.2: identifies situations with independent or dependent events in an experiment, simulation, or situation, e.g., There are three marbles in a bag. If you draw one marble and give it to your brother, and another marble and give it to your sister, are these independent events or dependent events?

Independent and Dependent Events

4.1.3: finds the probability of a compound event composed of two independent events in an experiment, simulation, or situation, e.g., what is the probability of getting two heads, if you toss a dime and a quarter?

Independent and Dependent Events

Theoretical and Experimental Probability

4.1.4: finds the probability of simple and/or compound events using geometric models (spinners or dartboards).

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

4.2.1: organizes, displays and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including a title, labels, categories, and rational number intervals using these data displays:

4.2.1.a: frequency tables;

4.2.1.b: bar, line, and circle graphs;

Reaction Time 1 (Graphs and Statistics)

4.2.1.d: charts and tables;

4.2.1.e: stem-and-leaf plots (single and double);

4.2.1.f: scatter plots;

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

4.2.1.g: box-and-whiskers plots;

4.2.1.h: histograms.

Histograms

Stem-and-Leaf Plots

4.2.2: recognizes valid and invalid data collection and sampling techniques.

Polling: City

Polling: Neighborhood

Populations and Samples

4.2.6: makes a scatter plot and draws a line that approximately represents the data, determines whether a correlation exists, and if that correlation is positive, negative, or that no correlation exists.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.